Question

if sec 5A is equal to cosec (A + 30) find A

Answer 1

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Answer 2

$We \: have, \: \: \: \: \: \: sec \: 5A = cosec(A + {30}^{o}) \\ ⇒sec \: 5A = sec \: [{90}^{o} - (A + {30}^{o} )] \\ [∵sec \: {90}^{o} - ϑ) = cosec \: \: ϑ] \\ ⇒sec \: 5A = sec( {60}^{o} - A) \\ ⇒5A = {60}^{o} - A \\ [∵ \: 5A \: and \: ( {60}^{o} - A) \: are \: acute \: angles] \\ ⇒ \: 6A = {60}^{o} \\ ∴ \: A = {10}^{o}$